GATE EE 2019 Set 1 — Question 30
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Electromagnetic Fields → Electrostatics → Capacitance
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Question
A co-axial cylindrical capacitor shown in Figure (i) has dielectric with relative permittivity . When one-fourth portion of the dielectric is replaced with another dielectric of relative permittivity , as shown in Figure (ii), the capacitance is doubled. The value of is _______.
Correct answer
9 to 11
Solution
The capacitance of a coaxial capacitor is given by . Let . In Figure (i), the capacitance is . In Figure (ii), the capacitor is split angularly into two parallel capacitors: one with of the original dielectric and one with of the new dielectric. The new capacitance is , where . Given , we have .
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